Gholipour, Kermani and Zamanian (2020) built a pore-network model (PNM) of the cathode gas diffusion layer (GDL) of a polymer-electrolyte-membrane fuel cell (PEMFC), coupled to network models of oxygen and electron transport and to simplified catalyst-layer and membrane submodels, and used it to predict flooding-related performance losses. The model treats water strictly as pure vapor (dry case) or pure liquid (wet case), is isothermal, excludes the gas channel, and was run at a single operating point (0.75 A/cm², fully humidified cathode). Its published outlook asks for: a heat-conduction network through the solid fibers and stagnant fluid phases plus a pore-scale phase-change model so liquid and vapor water are transported simultaneously under realistic thermal gradients; coupling to a gas-channel two-phase flow model resolving droplet formation and detachment at the GDL-channel interface; systematic investigation of GDL morphological properties (pore-size-distribution width, coordination number, fiber-orientation anisotropy, compression ratio) on coupled flooding and performance metrics; and extension across current densities and relative humidities to map where flooding becomes performance-limiting. The integrated modeling objective is that no single GDL pore-network model at normal operating temperatures yet closes the GDL-gas-channel boundary condition with a two-phase channel model resolving droplet formation and detachment, nor uses such an integrated model to produce the requested morphology and operating-condition maps.

Background

A polymer-electrolyte-membrane fuel cell (PEMFC) converts hydrogen and oxygen into electricity through electrochemical reactions. On the cathode, the oxygen-reduction reaction at the catalyst layer (CL, a thin porous film of platinum catalyst on carbon) produces water, while oxygen must diffuse in from the gas flow channels. Between the CL and the channels sits the gas diffusion layer (GDL) — a roughly 100–300 μm sheet of hydrophobized carbon-fiber paper, often coated on the CL side with a finer microporous layer (MPL) — which must simultaneously let oxygen pass toward the CL and let product water escape toward the channel. If too much liquid water accumulates in the GDL ("flooding"), oxygen pathways are blocked and the limiting current (the current at which oxygen transport can no longer sustain the reaction) drops; if the membrane dries out, proton conduction degrades. This water-management trade-off is a central PEMFC engineering problem.

A pore-network model (PNM) represents the GDL as a network of pore bodies connected by narrower throats, with capillary entry pressures (the pressure difference a phase must exceed to invade a throat, set by interfacial tension, throat radius, and wettability) and phase conductances (the ease with which each phase flows through a throat) assigned from pore geometry; two-phase algorithms (quasi-static invasion percolation, i.e. successive pore filling in order of capillary entry pressure, or dynamic network models that also track viscous pressures) then simulate how liquid water invades the initially gas-filled network. The coordination number (the average number of throats meeting at a pore), the pore-size-distribution width, fiber-orientation anisotropy, and the compression ratio (how much the GDL is squeezed under the current-collector ribs during stack assembly) together characterize the network morphology.

Gholipour, Kermani and Zamanian (2020) developed a GDL PNM coupled to network models of oxygen and electron transport through the GDL and to simple CL and membrane submodels, so that water generation, reactant access, and charge transport interacted in a single transient simulation up to steady state. The model predicted strongly non-uniform water saturation (local liquid-filled volume fraction) with maxima under the current-collector ribs, a 38.8% reduction of the limiting current caused by water blockage, and concentration overvoltage (voltage loss from reactant depletion) concentrated in the under-rib region. The source's stated limitations are: water enters and crosses the GDL either as pure vapor (dry case) or pure liquid (wet case), with no phase change, no temperature gradients, and no heat transport; the gas channel is not part of the model; only one operating point was simulated; and one network realization cost 30–80 hours on a single CPU core.

These simplifications matter physically. Waste heat released near the catalyst layer drives a through-plane thermal gradient, and in a real cell water crosses the GDL in both phases at once: liquid evaporates in warmer regions and vapor condenses elsewhere, so the dry/wet dichotomy cannot represent the actual water pathway. Moreover, liquid reaching the GDL–channel interface forms droplets that grow and detach into the air stream, and this detachment process sets the boundary condition for drainage of the GDL. The task therefore targets the closure of the GDL-channel boundary condition by a two-phase channel model resolving droplet formation and detachment, integrated within a single GDL pore-network framework, together with the systematic morphology and operating-condition mapping.

Problem Statement

Extend the coupled pore-network modeling framework of Gholipour, Kermani and Zamanian (2020) for the cathode gas diffusion layer of a PEMFC so that, within a single model: (1) heat conduction is solved on the network through both the solid fiber walls and the stagnant fluid phases, together with pore-scale evaporation and condensation, so that liquid water and water vapor are transported simultaneously under the thermal gradients present near the catalyst layer — replacing the current dichotomy of a pure-vapor dry case and a pure-liquid wet case; (2) the boundary condition at the GDL-gas-channel interface is closed by coupling the pore network to a two-phase flow model of the gas channel that resolves droplet formation and detachment; and (3) the coupled model is exercised systematically to determine how GDL morphological properties — pore-size-distribution width, coordination number, fiber-orientation anisotropy, and compression ratio — and operating conditions — current density and cathode relative humidity, beyond the single 0.75 A/cm² fully humidified point — affect the coupled flooding and performance metrics (water saturation distributions, limiting current, concentration overvoltage), and to map — in terms of these metrics — the operating envelope in which liquid-water flooding becomes performance-limiting. The threshold at which flooding counts as performance-limiting is to be defined by the solver in terms of these same metrics — for example, a fractional reduction of the limiting current or a rise in concentration overvoltage attributable to liquid-water blockage — and stated together with the current-density and cathode-relative-humidity range and resolution at which the maps are produced. The present cost of such simulations (30-80 CPU-hours per realization on a single core) means algorithmic improvements or reduced-order representations are an accepted enabling route to the parametric maps, not a separate deliverable. The requested result is the integrated model together with the morphology and operating-condition maps it produces.

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